Bernadette Perrin-Riou
We associate to a filtered $\varphi$-module $D$ a sub-$Z_p[[x]]$-module of convergent series on the open unit disk in which the $p$-adic $L$-functions of the Galois representation associated to $D$ and the $Z_p$-cyclotomic extension live…
We come back to the construction of p-adic L-functions attached to cusp forms of even weight k in the spirit of G. Stevens, R. Pollack [7] and M. Greenberg [3] with a new unified presentation including the non-ordinary case. This…
The article revisits a result of Antonio Lei, David Loeffler, and Sarah Livia Zerbes concerning the structure of the image by the Iwasawa regulator map of the Iwasawa module associated with a semi-stable $p$-adic representation on an…
We revisit some papers by Eichler and Shimura in order to give an algebraic formulation (based on Farey symbols) for the intersection product on the space of modular symbols, as described by Pollack and Stevens. We define the period…
A few pages in Siegel describe how, starting with a fundamental polygon for a compact Riemann surface, one can construct a symplectic basis of its homology. This note retells that construction, specializing to the case where the surface is…
We revisit the calculation of the strong Weil curve in an isogeny class of elliptic curves over Q, of the Manin constant and modular degree of an elliptic curve, using modular symbols as defined in [Pollack-Stevens], now implemented in…
We review the main conjecture for an elliptic curve on $\Q$ having good supersingular reduction at $p$ and give some consequences of it. Then we define the notion of $\lambda$-invariant and of $\mu$- invariant in this situation,…
Let V be a crystalline p-adic representation of the absolute Galois group G_K of an finite unramified extension K of Q_p and T a lattice of V stable by G_K. We prove the following result: Let Fil^1 V be the maximal sub-representation of V…
Nekov\'a\v{r} vient de d\'emontrer que le rang de $E(\Q)$ pour une courbe elliptique $E$d\'efinie sur $\Q$ est de m\^eme parit\'e que la multiplicit\'e du z\'ero en $s=1$ de la fonction $L_{E}$ complexe associe\'e \`a $E/\Q$, lorsque le…